1. If a certain amount of money doubles in \(n\) years at a fixed annual compound interest rate, then in how many years will it become four times?

2. If a certain amount of money doubles in \(n\) years under a fixed annual compound interest rate, in how many years will it become 4 times its original value?

3. If a sum of money becomes 4 times its original amount in *n* years at a fixed annual compound interest rate, then in how many years will it become 4 times?

4. If a sum of money doubles in \(n\) years at a fixed annual compound interest rate, then in how many years will it become 4 times?

5. If a certain amount of money doubles in \(n\) years at an annual compound interest rate, determine in how many years it will become eight times.

6. If a certain amount of money triples in 7 years at an annual compound interest rate, in how many years will it become 9 times?

(a) 10 (b) 12 (c) 14 (d) 13

7. If a principal amount doubles in 8 years at an annual compound interest rate of \(r\%\), then in how many years will it become four times?

8. If a certain amount of money triples in 11 years at a fixed interest rate, in how many years will it become five times?

(a) 12 years (b) 6 years (c) 20 years (d) 22 years

9. Determine how many years it will take for an amount to become eight times its original value under a fixed annual compound interest rate, given that it doubles in \(n\) years.

10. If a sum of money doubles in \(n\) years at an annual compound interest rate, then it will become four times in –

(a) \(2n\) years (b) \(\cfrac{n}{2}\) years (c) \(3n\) years (d) \(\cfrac{n}{3}\) years

11. If a certain amount of money triples in 20 years with interest and principal, in how many years will it become six times?

(a) 40 years (b) 60 years (c) 50 years (d) 30 years

12. If ₹27,500 doubles in 6 years at compound interest, then in how many years will it become four times?

(a) 16 (b) 15 (c) 12 (d) 10

13. A principal amount doubles in 20 years at a certain simple interest rate. At the same rate, in how many years will the principal become three times?

14. At an annual compound interest rate of 10%, in how many years will ₹4000 amount to ₹5324? Let’s calculate and write it down.

15. If a certain amount of money triples in 20 years, then at the same simple interest rate, in how many years will it double?

16. A farmer deposited some money in the village post office. After 4 years, he found that the total amount including interest had become ₹434. He calculated that the interest he received was \(\frac{6}{25}\) of his principal amount. Find how much money he had originally deposited and what annual rate of simple interest the post office gave.

17. At an annual simple interest rate of 18%, in how many years will a principal amount become 6 times its original value?

(a) 25 years (b) 30 years (c) 31.78 years (d) 27.78 years

18. If a certain amount of money grows to ₹12,100 in 3 years and ₹14,641 in 5 years at a compound interest rate, what is the annual interest rate?

(a) 10% (b) 15% (c) 5% (d) 12%

19. At an annual compound interest rate of 20%, in how many years will ₹1000 amount to ₹1440?

20. If a principal amount doubles in 20 years at a certain simple interest rate, then in how many years will it triple at the same simple interest rate?

21. At an annual compound interest rate of 4%, in how many years will a principal amount of ₹40,000 accumulate to ₹46,656?

22. At an annual simple interest rate of 5.25%, Shova Devi deposited a certain amount of money in a bank. After 2 years, she received ₹840 as interest. Calculate how much money she had deposited.

23. Rahmat Chacha deposited a certain amount of money in a cooperative bank at an annual compound interest rate of 9%. After 2 years, he received ₹29,702.50 as the total amount (principal + interest). Let us determine how much money Rahmat Chacha originally deposited in the cooperative bank.

24. Let us determine in how many years ₹40000 will amount to ₹46656 at an annual compound interest rate of 8%.

25. Calculate and write in how many years ₹300000 will amount to ₹399300 at an annual compound interest rate of 10%.

26. At an annual interest rate of 4%, for how much money will the difference between the simple interest and the compound interest for 2 years be 80 rupees? Let’s calculate and write it down.

27. Under the condition that no interest will be charged if the money is repaid within two years, three friends borrowed ₹6000, ₹8000, and ₹5000 respectively from a cooperative bank to jointly purchase four cycle rickshaws. After two years, after deducting all expenses, their total income amounted to ₹30,400. They divided this income in proportion to their capital contributions and then repaid their individual bank loans. Now, calculate how much money each person will have left in hand and what the ratio of the remaining amounts will be.

28. If a principal amount doubles in 4 years at a compound interest rate of \(r\%\), then it will become 4 times in ______ years.

29. If a machine’s value depreciates at a fixed annual rate and becomes \(\frac{1}{2}\) of its original value in 5 years, then in how many years will it become \(\frac{1}{4}\) of its original value?

30. At an annual simple interest rate of 5%, how many years will it take for the interest on ₹6000 to become ₹1500?

(a) 3 years (b) 30 years (c) 5 years (d) 15 years